While the fonts and the respective packages are being built, as pragmatic as it can be, one can get away with the following inline TikZ drawings
\documentclass{article}
\usepackage{tikz}
\newcommand{\dflat}{\tikz[baseline=-1.2mm] \node {\reflectbox{$\flat$}};}
\newcommand{\sflat}{\tikz[baseline=-1.2mm] \node {\reflectbox{$\flat$}$\flat$};}
\newcommand{\dsharp}{\hskip3pt \tikz[baseline=-1.2mm] {%
\clip (-2pt,-6pt) rectangle (-.2pt,6pt); \node at (0,0) {$\sharp$};}\hskip3pt
}
\newcommand{\ssharp}{\tikz[baseline=-1.2mm] {%
\node[inner sep=0mm] at (0,0) {$\sharp$};\node at (1.7pt,0.55pt) {$\sharp$};}
}
\begin{document}
\parbox{5cm}{
This is some random text to use the symbols \dflat, \sflat,\dsharp and \ssharp inline.
It can be improved by assigning some input parameters and adjusting the kerning as
C~{\hskip-7pt\dflat}, A~{\hskip-6pt\dsharp} or D~{\hskip-6pt\ssharp}
}
\end{document}

I will not attempt to make stupid comments since I know almost nothing about typography and kerning but this can be automated at will. Also I am not sure if these commands I have defined are robust. Please consider this as a proof of concept.
Addition by Jake:
By using \tikz [baseline] \node [anchor=base, inner sep=0pt]
, the nodes will automatically be positioned on the text line like a character would, so the vertical position doesn't have to be adjusted manually.
When defining TikZ commands to be used in text lines, it is usually a good idea to specify lengths in terms of ex
and em
, since these depend on the surrounding font size. That way, the symbols will scale with the text.

\documentclass{article}
\usepackage{tikz}
\newcommand{\dflat}{\tikz [baseline] \node [anchor=base, inner sep=0pt] {\reflectbox{$\flat$}};}
\newcommand{\sflat}{\tikz [baseline] \node [anchor=base, inner sep=0pt] {\reflectbox{$\flat$}$\flat$};}
\newcommand{\dsharp}{\tikz [baseline] {%
\clip (-0.2em,-1ex) rectangle (-0.01em,2ex);
\node[anchor=base, inner sep=0pt] {$\sharp$};}
}
\newcommand{\ssharp}{\tikz[baseline] {%
\node[anchor=base,inner sep=0pt,name=leftsharp] at (0,0) {$\sharp$};
\node at (leftsharp.east) [xshift=-0.25em, yshift=0.1ex, inner sep=0pt,anchor=west] {$\sharp$};}
}
\begin{document}
\parbox{5cm}{
This is some random text to use the symbols \dflat, \sflat, \dsharp and \ssharp inline.
It can be improved by assigning some input parameters and adjusting the kerning as
C\dflat, A\dsharp or D\ssharp
}
\parbox{5cm}{\Large
The symbols scale with the text:
C\dflat, A\dsharp or D\ssharp
}
\end{document}
The quarter note symbol from package wasysym
can be used without loading the package:
\documentclass{article}
\providecommand*{\quarternote}{%
\begingroup
\fontencoding{U}%
\fontfamily{wasy}%
\selectfont
\symbol{12}%
\endgroup
}
\begin{document}
\tiny \quarternote
\scriptsize \quarternote
\small \quarternote
\normalsize \quarternote
\large \quarternote
\Large \quarternote
\LARGE \quarternote
\huge \quarternote
\Huge \quarternote
\end{document}

I would not recommend \Vier
of package harmony
, because it is a constructed symbol at a fixed font size.
The following file compares the the quarter note symbols from wasy
and arev
and removes a substitution warning from the wasy
symbol if \bfseries
is used
(Only sizes smaller 10pt are not available as bold).
\documentclass{article}
% wasy
\newcommand*{\quarternotewasy}{%
\begingroup
\fontencoding{U}%
\fontfamily{wasy}%
\fontshape{n}%
\ssubSeriesBXtoB
\selectfont
\symbol{12}%
\endgroup
}
\makeatletter
\newcommand*{\ssubSeriesBXtoB}{%
\if b\expandafter\@car\f@series{}\@nil
\fontseries{b}%
\fi
}
\makeatother
% arev
\newcommand*{\quarternotearev}{%
\begingroup
\usefont{U}{zavm}{m}{n}%
\symbol{90}%
\endgroup
}
\newcommand*{\test}[2]{%
#2%
\tiny #1%
\scriptsize #1%
\small #1%
\normalsize #1%
\large #1%
\Large #1%
\LARGE #1%
\huge #1%
\Huge #1%
}
\begin{document}
\begin{tabular}{ll}
wasy: & \test{\quarternotewasy}{} \\
wasy-bold: & \test{\quarternotewasy}{\bfseries} \\
arev: & \test{\quarternotearev}{} \\
\end{tabular}
\end{document}

Best Answer
Are you including the appropriate packages?
See LaTeX Comprehensive symbols list.